When a signal is Fourier Transformed it is expressed in terms of a set of harmonically related phasors which can be graphically represented by the spectrum. Each harmonic of the spectrum has a specific amplitude, phase and frequency. Scaling in frequency of the spectrum corresponds to the inverse scaling in time of the signal. A common illustration is the effect on the frequency content that results when an audio tape is recorded at one speed and played back at a different speed. If the playback speed is higher than the recording speed, then the frequency is scaled up, which corresponds to compression in time and vice versa. In practice this inverse relation between time and frequency may be valuable for several situations in the field of electrical systems. For instance, high speed single shot events are difficult to capture and record numerically using present day analog-to-digital converters. By down scaling all the frequencies of the spectrum, the signal can be stretched in time and then recorded in numerical form using conventional technology.
The technique of spectrum scaling is well known in signal processing and conditioning systems. It is understood that the techniques rely on the scaling of the Fourier Transform relation which is difficult to implement on real time for high speed signals due to the large computational time involved in the Fast Fourier Transform algorithms. In one form, the invention disclosed herein provides a means to achieve real time spectrum scaling, both for down conversion and up conversion, and is easy to implement due to few active electrical components. A Doppler effect is used in the technique together with graphical illustrations and associated mathematical analysis to describe the methods and apparatus of the invention.